Stress-controlled carbon diffusion channeling in bct-iron: A mean-field theory

Abstract

Diffusion of interstitial carbon atoms in iron is the rate-limiting phenomenon of a number of phase transitions in body-centered (bec) and body-centered tetragonal (bct) phases such as ferrite and martensite. These phases being rarely stress-free and undeformed, the influence of stress/strain on the diffusivity of carbon is essential, although scarcely documented. We developed a model of carbon elastodiffusion in bct-iron. We combined anisotropie linear elasticity theory of point defects, the dilute approximation of regular solutions and the multisite model of random walk into a coherent mean-field theory. The model allows predicting the effects of composition, temperature and mechanical loading on the anisotropy of carbon diffusion. Density functional theory calculations have provided most of the materials parameters. The predictions were successfully tested against kinetic Monte Carlo simulations. Our results show that compression of the crystal increases carbon diffusivity, while tension has the opposite effect. Axial straining is accompanied by a large anisotropy of diffusion. This effect could be exploited to produce stress-controlled diffusion channeling for the engineering of anisotropie micro structures during thermal ageing of martensitic Fe-C alloys.

Effect of stress on vacancy formation and diffusion in fcc systems: Comparison between DFT calculations and elasticity theory

“…Equations presented below are inspired from the work of Maugis et al [13] and derive from the linear elasticity theory of point defects [26,27]. The effect of an applied strain or stress can be achieved using two quantities: the elastic dipole tensor of the point defect (vacancy or transition state), P, and the rank-4 stiffness tensor of the lattice, C. They were both computed using DFT calculations, as detailed in section 4.…”

“…Moreover, such an approach can also be used to predict the effects of com-position, temperature and mechanical loading on solubility and diffusivity. It has been carried out in the specific case of carbon insertion in iron [12,13]. This is interesting because, in a bcc-Fe system, carbon insertion induces strongly anisotropic elastic tensor with high values.…”

Theoretical study on hydrogen solubility and diffusivity in the γ-TiAl L10 structure

“…Due to the symmetry of the system, diagonal components are not equivalent in all directions, just as C atoms in iron [42,43]. Components are smallest ( < 1.2eV) in the case of 1c sites, elastic effects are thus minimal.…”

Stability of Zener order in martensite: an atomistic evidence

“…On the theoretical side, investigations of carbon ordering in iron involved various techniques: thermodynamic meanfield modelling [12,13,14,15,16], the microscopic elasticity theory [4,10,17,18,19], the CALPHAD formalism [20,21], molecular dynamics [22,23,14,24] and combined ab initio-Monte Carlo [25,26,16,27]. Most of these approaches, although based on di erent hypotheses and approximations, provide results in favour of Zener ordering.…”

“…⌘ > 0, ⇣ = 0, > 0; Zener order), tetragonal oblate (e.g. ⌘ < 0, ⇣ = 0, < 0; inverse-Zener order [27,26]) or orthorhombic (e.g. ⌘ ë 0, ⇣ ë 0; beyond-Zener order [30,4]).…”